Codeforces Global Round 18 |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

binary search

constructive algorithms

data structures

divide and conquer

flows

graphs

shortest paths

*3000

No tag edit access

The problem statement has recently been changed. View the changes.

×
H. Reindeer Games

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere are $$$n$$$ reindeer at the North Pole, all battling for the highest spot on the "Top Reindeer" leaderboard on the front page of CodeNorses (a popular competitive reindeer gaming website). Interestingly, the "Top Reindeer" title is just a measure of upvotes and has nothing to do with their skill level in the reindeer games, but they still give it the utmost importance.

Currently, the $$$i$$$-th reindeer has a score of $$$a_i$$$. You would like to influence the leaderboard with some operations. In an operation, you can choose a reindeer, and either increase or decrease his score by $$$1$$$ unit. Negative scores are allowed.

You have $$$m$$$ requirements for the resulting scores. Each requirement is given by an ordered pair $$$(u, v)$$$, meaning that after all operations, the score of reindeer $$$u$$$ must be less than or equal to the score of reindeer $$$v$$$.

Your task is to perform the minimum number of operations so that all requirements will be satisfied.

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$2\le n\le 1000$$$; $$$1\le m\le 1000$$$) — the number of reindeer and requirements, respectively.

The second line contains $$$n$$$ integers $$$a_1,\ldots, a_n$$$ ($$$1\le a_i\le 10^9$$$), where $$$a_i$$$ is the current score of reindeer $$$i$$$.

The next $$$m$$$ lines describe the requirements.

The $$$i$$$-th of these lines contains two integers $$$u_i$$$ and $$$v_i$$$ ($$$1\le u_i, v_i\le n$$$; $$$u_i\ne v_i$$$) — the two reindeer of the $$$i$$$-th requirement.

Output

Print $$$n$$$ integers $$$b_1,\ldots, b_n$$$ ($$$-10^{15}\le b_i\le 10^{15}$$$), where $$$b_i$$$ is the score of the $$$i$$$-th reindeer after all operations.

If there are multiple solutions achieving the minimum number of operations, you may output any.

We can prove that there is always an optimal solution such that $$$|b_i|\le 10^{15}$$$ for all $$$i$$$.

Examples

Input

7 6 3 1 4 9 2 5 6 1 2 2 3 3 4 4 5 5 6 6 7

Output

1 1 4 4 4 5 6

Input

4 6 6 5 8 2 3 1 4 1 3 2 1 2 2 3 3 1

Output

6 6 6 2

Input

10 18 214 204 195 182 180 176 176 172 169 167 1 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 6 1 6 2 6 3 6 4 6 5 6 7 6 8 6 9 6 10

Output

204 204 195 182 180 167 176 172 169 167

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/06/2024 17:16:11 (k2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|